JEE Mains 2025 Shift 1 Physics PDF

JEE Main – 22nd January – 2025 (Shift -1) [Memory Based Questions] PHYSICS 1. A Parallel plate capacitor of capacitance 40µF is connected to a 100V power supply now the intermediate space between the plates is filled with a diele...

JEE Main – 22nd January – 2025 (Shift -1) [Memory Based Questions] PHYSICS 1. A Parallel plate capacitor of capacitance 40µF is connected to a 100V power supply now the intermediate space between the plates is filled with a dielectric material of dielectric constant k=2. due to the introduction dielectric the extra charge and the change in electrostatic energy in the capacitor respectively of a) 2 mC and 0.4J b) 2 mC and 0.2 J c) 4 mC and 0.2J d) 8 mC and 2J Ans: (c) 2. A uniform circular disc of radius 'R' and mass 'm' is rotating about an axis perpendicular to it's plane & passing through it's center. A small circular part of radius R/2 is removed from the original disc as shown in the figure. Find moment of inertia of the remaining part of the original disc about the axis as given above 17 15 7 13 a) mR2 b) mR2 c) mR2 d) mR2 32 32 32 32 Ans: (d) 3. An electron in the ground state of the hydrogen atom has the orbit, radius of 5.3 × 10−11 m while that for the electron in third excited state is 8.4 8 × 10−10 m. The ratio of the de-Broglie wavelength is of electron in the ground state to that in the excited state is a) 9 b) 3 c) 4 d) 16 Ans: (c) 1  B 4. Find the dimensions of μ0 a) [AL] b) [AL-1] c) 3 [MAL] d) [MALT-1] Ans: (b) 5. Solid sphere of mass M, radius R exerts force F on a point mass. Now a concentric M spherical mass is removed. What is new force? 7 F 6F 5F 3F a) b) c) d) 7 7 7 7 Ans: (b) 6. Given below are two statements: one is labelled as Statement I and the other is labelled as Statement II. Statement I- In a Vernier Caliper’s, one Vernier scale division is smaller than one main scale division. Statement II- The Vernier constant is given by one main scale division multiplied by the number of Vernier scale divisions. In the light of the above statements, choose the correct answer from the options given below. a) Statement I is false but Statement II is true. b) Both Statement I and Statement II are true and Statement II is the correct explanation of Statement I. c) Both Statement I and Statement II are true but Statement II is not the correct explanation of Statement I. d) Statement I is true but Statement II is false. Ans: (d) 7. A bob of mass m is suspended at a point ‘O’ by a light string of length 'l' and left to perform vertical motion (circular) as shown in figure. Initially by applying horizontal velocity V0 at the point 'A’, the string becomes slack when the bob reaches at the point 'D'. The ratio of the K.E of the bob at the points B and C is a) 2 b) 4 c) 1 d) 3 Ans: (a) 2 8. Ice at −10∘ C is to be converted into steam at 110∘ C. Mass of ice is 10−3 kg. What amount of heat is required? a) ΔQ = 730cal b) ΔQ = 900cal c) ΔQ = 1210cal d) ΔQ = 870cal Ans: (a) 9. Given is a thin convex lens of glass (refractive index μ) and each slop having radius of carvature R. one side is polished for complete reflection. At what distance from the lens, an object be placed and the optic axis so that the image sets formed on the object itself? a) μR b) R/(2μ − 3) c) R/(2μ − 1) d) R/μ Ans: (c) 10. An electron is made to enter symmetrically b/w two parallel and equal oppositely charged metal plates, each of 10 cm length. The electron emerges out of the electric field region with a horizontal component of velocity 106 m/s. if the magnitude of the electric field between the plates is 9.1V/cm, then the vertical component of velocity of electron is (mass of electron = 9.1 × 10−31 kg, and charge of electron = 1.6 × 10−19 C). a) 0 b) 16 × 106 m/s c) 16 × 104 m/s d) 1 × 106 m/s Ans: (b) 11. The work functions of cesium (Cs) and lithium (Li) metals are 1.9eV & 2.5 CV, respectively. If we incident a light of wave length 550 nm on these two metal surface, then photo-electric effect is possible for the case of a) Cs only b) Both Cs and Li c) Li only d) Neither Cs nor Li Ans: (a) 12. A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities ρ1 and ρ2, respectively. The frequency of 9th harmonic of closed tube is identical with 4th harmonic of open tube. If the length of the closed tube is 10cm and the density ratio of the gases is ρ1: ρ2 = 1: 16, then the length of the open tube is: 15 20 15 20 a) cm b) cm c) cm d) cm 7 7 9 9 Ans: (d) 13. A small point of mass m is placed at a distance 2R from the center of a big uniform solid sphere of mass ‘m’ and radius R. The gravitational force on 'm' due to ‘m’ is F1. A spherical part of radius R/3 is removed from big sphere as shown in the figure and the gravitational force on m due to remaining part of m is found to be F2. The value of ratio F1: F2 is a) 16:9 b) 12:11 c) 11:10 d) 12:9 Ans: (b) 3 14. Two spherical black bodies of the radii 0.2cm and 0.4cm are at temperature 400K and 800K respectively. If the energy radiator by small body is E then energy radiated by large body is a) E b) 16E c) 64E d) 4E Ans: (c) 15. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: If young's double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer. Reason R: The speed of light reduces in an optically denser medium than air while its frequency does not change. In the light of the above statements, choose the correct answer from the options given below. a) A is false but R is true. b) Both A and R are true. c) Both A and R are false. d) A is true but R is false. Ans: (b) 16. Find current in the circuit. Jockey is at middle point on 1Ω Ans: 1A 4  CHEMISTRY 1. Which of the following lanthanide ion as 7 electrons in the outer most shell a) Eu+3 b) Gd+3 c) Eu+4 d) Gd+2 Ans: (b) 2. Number of linear compounds ? 𝐼3− , NO2 , O3 , OF2 , NO+ − 2 , BeCl2 , N3 , SO3 , CO2 , XeF2 a) 5 b) 2 c) 4 d) 3 Ans: (c) 3. Given the weight of the organic compound. 180 g and the weight of the AgCl precipitated 143.5 g. Calculate the percentage of Cl in the organic compound ? [wt of Cl = 35.5 g, wt of Ag = 108 g]. a) 13.20% b) 22.20% c) 35.20% d) 19.72% Ans: (d) 4. Electrolysis of which compound give H2S2O8 a) Electrolysis of Conc.Na2SO4 b) Electrolysis of Dil.Na2SO4 c) Electrolysis of Conc.H2SO4 d) Electrolysis of Dil.H2SO4 Ans: (c) 5. Which of the following electronegativity order is incorrect? a) Mg < Be < B < N b) Al < Si < C < N c) S < Cl < O < F d) Al < Mg < B < N Ans: (d) 6. Which of the following statement is not true for radioactive decay? a) Decay constant does not depend upon temperature b) Decay constant increases with increase in temperature 1 c) Half life is In 2 times of rate constant d) Amount of radioactive substance remained after three half lives is 1/8th of original amount Ans: (a) 7. (I) 10−4 NaCl, (II) 10−3 NaCl, (III) 10−2 NaCl, (IV) 10−4 Urea order of increasing B.P. a) I > II > III > IV b) III > II > I > IV c) II > I > III > IV d) III > I > II > IV Ans: (b) 5 8. Which of the following acids is a Vitamin. a) Saccharic acid b) Aspartic acid c) Adipic acid d) Ascorbic acid Ans: (d) 9. How many different stereoisomers are Possible for the given molecule? CH3  CH CH  CH  CH3 | OH a) 4 b) 3 c) 2 d) 1 Ans: (a) 10. IUPAC name? a) 6-methoxy-2, 5-dimethyl-6-oxohexanoic acid b) 7-methoxy-3-methyl hexanoic acid c) 3-methoxy-5-methyl hexanoic acid d) 3-methoxy-5, 6-dimethyl-2-hexanoic acid Ans: (a) 11. Incorrect statement. a) Melting point of Cis 2-butene is greater than trans 2-butene b) 2-butene can have two geometrical isomers c) Dipole moment of cis 2-butene is greater than trans 2-butene d) In trans isomer identical groups are opposite direction Ans: (a) 12. Find molecular weight of A a) 123 b) 115 c) 215 d) 154 Ans: (d) 13. For [NiCl4 ]2− what is the charge on metal and shape of complex respectively? a) +2, Tetrahedral b) +2, Square planar c) +4, Tetrahedral d) +4, Square Planar Ans: (a) 6 14. The correct decreasing order of electronegativity is a) F > Cl > I > Br b) Cl > F > Br > I c) F > Cl > Br > I d) Br > F > I > Cl Ans: (c) 15. Which of the following has maximum size out of Al3+ , Mg 2+ , F − , Na+ a) Al3+ b) Mg2+ c) F– d) Na+ Ans: (c) 16. CO2 (g) + C(s) ⇌ 2CO(g). If initial pressure of CO2 is 0.6 atm and after equilibrium is established, total pressure is 0.8 atm. Then, find K p. a) 0.4 b) 0.2 c) 0.6 d) 0.8 Ans: (a) 17. Statement-l: CH3 − O − CH2 − Cl will show nucleophilic substitution by SN 1 mechanism in protic medium. Statement-II: – Cl will not undergo nucleophilic substitution via SN 2 mechanism easily. a) Statement-I and statement-II both are correct b) Statement-I and statement-II both are incorrect c) Statement-I is correct but statement-II is incorrect d) Statement-I is incorrect but statement-II is correct Ans: (a) 18. An electron of He+ is present in 3rd excited state. Find its de-Broglie wave length. a) 6.64Å b) 1.66Å c) 3.32Å d) 13.28Å Ans: (a) 19. Given : NH2 COONH4 ( s) ⇌ 2NH3 ( g) + CO2 ( g). If the partial pressure of CO2 gas at equilibrium is 0.4 atm and the total pressure is 1 atm, the value of K p at the same temperature is a) 0.027 atm3 b) 0.064 atm3 c) 0.144 atm3 d) 0.216 atm3 Ans: (c) 20. In a closed insulated container, a liquid is stirred with a paddle to increase the temperature which of the following is true? a) 𝑤 = 0, Δ𝐸 = 𝑞 ≠ 0 b) Δ𝐸 = 𝑤 ≠ 0, 𝑞 = 0 c) Δ𝐸 = 𝑤 = 0, 𝑞 ≠ 0 d) Δ𝐸 = 0, 𝑤 = 𝑞 ≠ 0 Ans: (b) 7 21. Match the column and choose the correct option Column-I (Properties) Column-II (Order) (A) Electronegativity (1) B Mg > Al (D) Electron affinity (4) Cl > F > Br > I a) A − 1, B − 2, C − 3, D − 4 b) A − 4, B − 3, C − 2, D − 1 c) A − 2, B − 3, C − 4, D − 1 d) A − 3, B − 2, C − 4, D − 1 Ans: (a) 22. If work function of Cs and Fr is 1.9 and 2.5 eV. It the light = 500 nm. which element will have have Photoelectric effect. a) Only Cs b) Only Fr c) Both Cs and Fr d) None of these Ans: (a) 8  MATHEMATICS 1. Let the triangle PQR be the image of the triangle with vertices (1,3), (3,1), (2,4) in the line 𝑥 + 2𝑦 = 2. If the centroid of PQR is the point (𝛼, 𝛽) then 15(𝛼 − 𝛽) is equal to a) 10 b) 15 c) 25 d) 22 Ans: (d) 2. Two balls are selected at random one by one without replacement from the bag containing 4 white and 6 black balls. If the probability that the first selected ball is black given that the second selected is also black, is m/n where gcd(𝑚, 𝑛) = 1, then 𝑚 + 𝑛 = ? a) 11 b) 14 c) 6 d) 27 Ans: (b) 3. From the English alphabets, 5 letters are chosen and are arranged in alphabetical order. The total number of ways in which the middle letter is 𝐌. a) 2167 b) 1276 c) 5148 d) 2053 Ans: (c) (2𝑛−1)(2𝑛+1)(2𝑛+3)(2𝑛+5) 1 4. ∑𝑛𝑟=1 Tr = , then lim ∑𝑛𝑟=1 (𝑇 ) = 64 n 𝑟 2 3 1 2 a) b) 4 c) d) 3 5 5 Ans: (a) 5. Let 𝑓(𝑥) be a real differentiable function such that 𝑓(0) = 1 and 𝑓(𝑥 + 𝑦) = 𝑓(𝑥)𝑓 ′ (𝑦) + 𝑓(𝑦)𝑓 ′ (𝑥) for all 𝑥, 𝑦 ∈ 𝑅. Then ∑100 𝑛=1 log 𝑒 𝑓(𝑛) = a)1212 b) 2312 c) 2050 d) 2525 Ans: (d) 2 +3 6. The Product of all solutions of the equation 𝑒 5(log𝑒 𝑥) = 𝑥 8 , 𝑥 > 0 is 1 1 8 2 a) 𝑒 3 b) 𝑒 5 c) 𝑒 5 d) 𝑒 3 Ans: (c) 7. Let the foci of the hyperbola be (1, 14) and (1, −12). It passes through the point (1,6) then length of its latus rectum is? a) 22/7 b) 2/3 c) 288/5 d) 1/13 Ans: (c) 9 8. The number of non empty equivalence relations on the set {1,2,3} is a) 6 b) 4 c) 5 d) 7 Ans: (c) 9. 𝑎1 , 𝑎2 , 𝑎3 … …... are positive terms of increasing GP if 𝑎1 𝑎5 = 28 & 𝑎2 + 𝑎6 = 29 then find 𝑎3 =? a) 246 b) 325 c) 125 d) 784 Ans: (d) 10. Using the principle values of the inverse trigonometric functions, the sum of maximum and minimum values of 16[(sec −1 𝑥)2 ] + (cosec −1 𝑥)2 ] a) 17 2 b) 22 2 c) 13 2 d) 35 2 Ans: (b) 11. Find the area inside the circle (𝑥 − 2√3)2 + 𝑦 2 = 12 and parabola 𝑦 2 = 2√3𝑥 a) 16 4 3  5 b) 16 4 11  4 c) 3 4 11  5 d) 16  6 Ans: (d) 1 12. Let x = x(y) be the solution of the differential equation y 2 dx + (x − 𝑦) dy = 0. If 𝑥(1) = 1 then 1 𝑥 (2) is equal to 1 −3 a) 3 + 𝑒 b) + 𝑒 c) 3-e d) +𝑒 2 2 Ans: (c) 13. Let 𝐴 = {1,2,3,4,5,6,7,8,9,10} and 𝐵 = {𝑚/𝑛: 𝑚, 𝑛 ∈ 𝐴}, 𝑚 < 𝑛 and gcd(𝑚, 𝑛) = 1. then 𝑛(𝐵) is equal to a) 29 b) 36 c) 31 d) 37 Ans: (c) 5 11 C2 r 1 14.  2r  2  r 0 211  1 211  1 213  3 213  5 a) b) c) d) 12 3 5 7 Ans: (a) 🔴JEE Main 2025 Paper Solutions (22nd Jan,1st Shift) | JEE Main 2025 Question Paper & Expected Cutoff Telegram: Contact @InfinityLearnJEE ***** 10